Domanda del libro di testo
Convert each radian measure to degrees. See Examples 2(a) and 2(b). 7π/4
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Ch. 3 - Radian Measure and The Unit Circle
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891
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TOC.tableOfContents
- Ch. R - Algebra Review381
- Ch. 1 - Trigonometric Functions188
- Ch. 2 - Acute Angles and Right Triangles168
- Ch. 3 - Radian Measure and The Unit Circle155
- Ch. 4 - Graphs of the Circular Functions100
- Ch. 5 - Trigonometric Identities238
- Ch. 6 - Inverse Circular Functions and Trigonometric Equations158
- Ch. 7 - Applications of Trigonometry and Vectors148
- Ch. 8 - Complex Numbers, Polar Equations, and Parametric Equations15
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891Non è quello che usi tu?Cambia libro di testo
Capitolo 4, Problema 31
The formula ω = θ/t can be rewritten as θ = ωt. Substituting ωt for θ converts s = rθ to s = rωt. Use the formula s = rωt to find the value of the missing variable.
s = 3π/4 km, r = 2 km, t = 4 sec
Guida verificata passo dopo passo1
Identify the given variables and the formula to use. Here, you have the arc length \(s = \frac{3\pi}{4}\) km, radius \(r = 2\) km, and time \(t = 4\) sec. The formula relating these is \(s = r \omega t\), where \(\omega\) is the angular velocity.
Write down the formula explicitly: \(s = r \omega t\). Since \(s\), \(r\), and \(t\) are known, you need to solve for \(\omega\).
Rearrange the formula to isolate \(\omega\): \(\omega = \frac{s}{r t}\).
Substitute the known values into the rearranged formula: \(\omega = \frac{\frac{3\pi}{4}}{2 \times 4}\).
Simplify the expression step-by-step to find the value of \(\omega\). Remember to keep the answer in terms of \(\pi\) unless asked otherwise.
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Concetti chiave
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Angular Displacement and Angular Velocity
Angular displacement (θ) measures the angle through which an object rotates, usually in radians. Angular velocity (ω) is the rate of change of angular displacement over time, expressed as ω = θ/t. Understanding this relationship allows conversion between angular and linear quantities.
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Percorso guidato
03:48
Introduction to Vectors
Arc Length Formula
The arc length (s) of a circle segment is the distance traveled along the circumference and is given by s = rθ, where r is the radius and θ is the angular displacement in radians. This formula connects linear distance with angular motion.
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Percorso guidato
4:18Finding Missing Side Lengths
Relating Linear and Angular Quantities
By substituting θ = ωt into s = rθ, we get s = rωt, linking linear distance (s), radius (r), angular velocity (ω), and time (t). This formula is essential for finding any missing variable when others are known in rotational motion problems.
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Percorso guidato
6:00Categorizing Linear Equations
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